Glasses having a low coefficient of thermal expansion (“CTE”) have applications in many different applications of space technology, astronomy, masks for EUV (extreme ultraviolet) lithography processes, optics, substrates and other uses. In many of these applications it is important to be able to construct large assemblies or structures using low CTE (CTE=5×10−7/° C. or less over the temperature range of −50° C. to +150° C.). Present methods of making large assemblies require fixturing pieces of low CTE glass together and heating the large part assembly in a large furnace environment to the point where the viscosity of the glass is sufficiently low that the glass pieces fuse together at their points of contact. While this method can make large assemblies it is essentially an “all-or-nothing” process.” If something goes wrong, for example, a part of the fixture moves or the temperature environment in the furnace is uneven; the entire assembly may be useless and have to be discarded. This is both costly and time consuming. As a result, it is highly desirable to have a method in which an assembly can be constructed from discrete parts. The present invention discloses a method for constructing an assembly from discrete parts which are thermally welded/joined using a laser and an apparatus for use in such method